Study of refractive structure in the inelastic $^{16}$O+$^{16}$O scattering at the incident energies of 250 to 1120 MeV

26 pages, 10 figures, Accepted for publication in Nucl. Phys. AThe data of inelastic 16O+16O scattering to the lowest 2+ and 3- excited states of 16O have been measured at Elab = 250, 350, 480, 704 and 1120 MeV and analyzed consistently in the distorted wave Born approximation (DWBA), using the semi- microscopic optical potentials and inelastic form factors given by the folding model, to reveal possible refractive structure of the nuclear rainbow that was identified earlier in the elastic 16O+16O scattering channel at the same energies. Given the known transition strengths of the 2+ and 3- states of 16O well determined from the (e,e') data, the DWBA description of the inelastic data over the whole angular range was possible only if the absorption in the exit channels is significantly increased (especially, for the 16O+16O(2+) exit channel). Although the refractive pattern of the inelastic 16O+16O scattering was found to be less pronounced compared to that observed in the elastic scattering channel, a clear remnant of the main rainbow maximum could still be seen in the inelastic cross section at Elab = 350 - 704 MeV